Skip to Main content Skip to Navigation
Journal articles

Inflating balls is NP-hard

Guillaume Batog 1 Xavier Goaoc 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : A collection C of balls in R^d is \delta-inflatable if it is isometric to the intersection U \cap E of some d-dimensional affine subspace E with a collection U of (d+\delta)-dimensional balls that are disjoint and have equal radius. We give a quadratic-time algorithm to recognize 1-inflatable collections of balls in any fixed dimension, and show that recognizing \delta-inflatable collections of d-dimensional balls is NP-hard for \delta \geq 2 and d \geq 3 if the balls' centers and radii are given by numbers of the form a+b\sqrt{c+d\sqrt{e}}, where a, ..., e are integers.
Document type :
Journal articles
Complete list of metadata

Cited literature [21 references]  Display  Hide  Download
Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Thursday, November 12, 2009 - 7:19:17 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Tuesday, October 9, 2012 - 1:51:02 PM


Files produced by the author(s)


  • HAL Id : inria-00331423, version 1



Guillaume Batog, Xavier Goaoc. Inflating balls is NP-hard. International Journal of Computational Geometry and Applications, World Scientific Publishing, 2008. ⟨inria-00331423⟩



Record views


Files downloads